Eur. Phys. J. Plus (2021) 136: 801
https://doi.org/10.1140/epjp/s13360-021-01811-3

Regular Article

Optimal control strategy for adherence to different treatment regimen in various stages of tuberculosis infection

Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, 711103, Howrah, West Bengal, India

^a akhatua06@gmail.com

Received: 27 April 2021
Accepted: 29 July 2021
Published online: 4 August 2021

Abstract

In this article, we propose a new mathematical model for tuberculosis considering the infectivity of both smear-positive and smear-negative individuals, searching for an efficient control strategy that may be followed to curtail the disease. We have employed different treatment regimens in various stages of tuberculosis infection. The fundamental epidemic threshold quantity $R_0$ is inspected by the next-generation matrix method. The forward normalized sensitivity indices of the model parameters connected with $R_0$ are computed to scale their impacts on the basic reproduction number. An optimal control problem is constructed considering three different treatment regimens in different possible stages of TB, and the control problem is solved analytically. The simulation results suggest that the combined implementation of all the controls optimally is the best policy to minimize the tuberculosis prevalence with the least interventions implementations costs.